How to connect a circle to a grid with even topology?
You are merging 2 meshes with very different densities. The circle is about double the subdivision compared to the rest. Your topology should look similar to this:




the 5 green polys (the E pole vertex in the middle) are responsible for the change in edge flow
both marked edgeloops should be nice and even to produce edges with consistent curvature alongside them


The goal is to use control mesh with the least amount of 3 or 5 edged vertices. Topology like that minimizes any surface artifacts (shows mostly on reflections)



I got this piece by using Shrinkwrap Modifier and projecting the geometry onto a subdivided cylinder.



To project 2 circles with Shrinkwrap onto a sphere is bit trickier, because we get this overlap, that has to be cleaned:



It's more elegant to prepare both pieces beforehand, so they line up together nicely when projected (the math of projecting onto sphere is not that complicated here). We cut each piece with an ellipse that has same width as the sphere, but has the minor axis of √2/2 (about 0.707):



I used the ellipse just as a guide to move and align vertices, but you can use Booleans to be exact.

Now it's easy to join the meshes perfectly:





If this is a mesh not to be sub-surfed, but a high-density game model, you can proceed the same way with a lower-poly control mesh and then apply the subsurface modifier at a level you like.

High-poly meshes are easy to sculpt or generate procedurally, but pain to model with precision.

If you keep a mesh with same size polygons, the smooth shading on it will also produce nice results, long triangles or long polygons do not behave nice. Your mesh from your question is very close to that state, with some cleanup I would call it fine. If you decide to use a normal map baked from the subsurfed high-poly, then even this stops being a problem, because the normals are now defined in a texture and you can have a mesh that looks however you like. The only concern becomes to have enough geometry so the silhouette looks clean.